Problem: Simplify the following expression: $r = \dfrac{9}{7q} + \dfrac{1}{6q}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7q$ and $6q$ $\lcm(7q, 6q) = 42q$ $ r = \dfrac{6}{6} \cdot \dfrac{9}{7q} + \dfrac{7}{7} \cdot \dfrac{1}{6q} $ $r = \dfrac{54}{42q} + \dfrac{7}{42q}$ $r = \dfrac{54 +7}{42q}$ $r = \dfrac{61}{42q}$